Download Pseudopotentials ≡ Effective Core Potential (ECP) Si 1s2 2s2 2p6

Pseudopotentials ≡ Effective Core Potential (ECP)
Si
1s2 2s2 2p6 3s2 3p2
Cu
1s2 2s2 2p6 3s2 3p6 3d104s
The inner electrons are not evolved in chemistry, and they make the
calculations expensive, because their presence requires large basis sets.
all-el.
C
Si
Cu
3s2p1d (14)
4s3p1d (18)
5s4p3d1f (39)
pseudo
2s2p1d
2s2p1d
3s3p2d
large
computational
savings
Actually, for an element such as Cu, there are different ways one can
do the core-valence split.
Core
I.
1s2 2s2 2p6
II.
1s2 2s2 2p6 3s2 3p6
III.
1s2 2s2 2p6 3s3 3p6 3d10
For Cu, I and II give similar quality results, but for other first-row transition
metal atoms, I may be preferable to II.
For Cu, III does not work well.
significant error in IP
about a factor of 2 error in De(Cu2).
The above comments pertain to the use of static ECPs.
Stoll and coworkers have developed polarizable-core ECPs. (In Molpro,
but not in G03).
with these, one can do quite well treating Cu as a “one electron atom”;
Obviously, can’t be used to describe d9 s2 excited states.
In GTO-based codes, ECPs are of the form:
U ECP (r ) = ∑ ai r e
ni
−α i r 2
i
Parameters generally chosen to reproduce orbital
energies from all-electron HF or DFT calculations
generally angular momentum dependent
For heavy elements, ECPs are usually chosen to reproduce the results
of all-electron relativistic calculations.
⇒ ECP calculations build in relativistic contraction!
NOTE: spin-orbit interactions are also a consequence of
relativistic effects.
These would still be needed to be treated explicitly,
even if using a relativistic ECP
The adoption of pseudopotentials is even more important for calculations
with plane-wave (eik•r) basis set
k and r are conjugate variables, related by Fourier transfer
rapid variations in orbitals at small r ⇒ need high k
basis sets would be prohibitively large without ECPs.